Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 5 - The Integral - 5.5 The Fundamental Theorem of Calculus, Part II - Exercises - Page 263: 29



Work Step by Step

By making use of Theorem 1 (FTC II), we have $$ \frac{d}{d x} \int_{0}^{x^{2}} \frac{t d t}{t+1}=\left(\frac{d}{d u} \int_{0}^{u} \frac{t d t}{t+1}\right)\frac{du}{dx}=\frac{x^2}{x^2+1} (2x)\\ =\frac{2x^3}{x^2+1}. $$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.